Mearth_attack - Visual Game

“We Martians come and conquer. We Martians interested and studied Mearth in years. MEarth must answer We Martians’ questions or Mearth be conquered. ” These were the alarming messages from the signals that the aliens transmitted to a satellite on Mearth. The signals were so advanced that only math language can interpret

“You are chosen, Young Heroes, to save Mearth and Mearthkind from the destructive plan of the Martians. Your heroic task is to answer correctly their questions on mathematics and earn points to reach the highest score.”

CLIC K ima ge

Yes, I am ready.

Q1 : 5 points 

Arithmetic: What is the value of 3 + 2*7 ? ( Here * denotes multiplication.)

17 20 35 13

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Q2 : 5 points 

Basic Algebra: Which of the following is equal to (2x - 7)^2 ?

4x^2 - 14x + 49 4x^2 - 28x + 49 4x^2 - 49 4x^2 + 49

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Q3 : 5 points 

Geometry: The perpendicular bisectors of the sides of a triangle are concurrent in this point.

The circumcenter The centroid The incenter The orthocenter

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Q4 : 5 points 

Analytic Geometry: e=0

What can you say about the eccentricity e of a hyperbola?

e=1 e is greater than 1 e is between 0 and 1

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Q5 : 10 points 

Linear Algebra: Let A be a square matrix with the property that there exists a positive integer k such that A^k is the zero matrix. A is said to be which of the following?

orthogonal idempotent symmetric nilpotent

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YOU HAVE EARNED

Q6 : 5 points 

Calculus: Suppose f(x) is a differentiable function for all real numbers x which also satisfies: f '(4) = 0, f '(x) is negative for all x less than 4, f '(x) is positive for all x greater than 4

What can be said about the critical value x = 4?

f(x) has a local maximum at x = 4 nothing can be said, we must use the second derivative test f(x) does not have a local extrema at x = 4 f(x) has a local minimum at x = 4

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Q7 : 5 points 

Advanced Calculus: The vector (xy, xz, yz) Let f(x,y,z) = xyz. What is the gradient of f?

The vector (xz, xy, yz) The vector (xz, yz, xy) The vector (yz, xz, xy)

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Q8 : 5 points 

Basic Set Theory: How many 2 element subsets does a 4 element set have?

12 4 6 3

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Q9 : 5 points 

Elementary Number Theory: Which of the following numbers is congruent to 3 mod 7?

27 17 37 47

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Q10 : 5 points 

Basic Probability: A box contains 2 good and 2 bad light bulbs. 2 light bulbs are selected from the box without replacement. Find the probability that both light bulbs selected were good.

1/2 2/3 1/4 1/6

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YOU HAVE EARNED a total of